The displacement $x$ of a particle varies with time $t$ as $x=a\left(1-e^{-\alpha t}\right)$, where

Question

The displacement $x$ of a particle varies with time $t$ as $x=a\left(1-e^{-\alpha t}\right)$, where $a$ and $\alpha$ are positive constants. The velocity of the particle will

Professor PC Thomas Classes · Answer

(b) : $x=a\left(1-e^{-\alpha t}ight)$ \ Velocity $v = \frac{d x}{d t}= a \alpha e^{-\alpha t}$ \ As time $t$ increases, the exponential term $e^{-\alpha t}$ continues to decrease. Thus, the velocity will go on decreasing with time.